A Frequency–Azimuth Spectrum Estimation Method for Uniform Linear Array Based on Deconvolution

Abstract

The frequency–azimuth (FRAZ) spectrum is a critical characteristic in passive target detection and tracking, as it encapsulates information regarding the signal’s frequency and azimuth. However, due to the inherent limitations in the sonar array’s physical aperture and the analysis time of the system, the signal often suffers from undersampling in both spatial and temporal dimensions. This undersampling leads to energy leakage across the azimuth and frequency domains, adversely affecting the resolution of the FRAZ spectrum. Such a reduction in resolution hampers multitarget resolution and feature extraction. To address these challenges, this study introduces a deconvolution-based FRAZ spectrum estimation method tailored for uniform linear arrays. The proposed method initiates by decoupling the azimuth and frequency in the FRAZ spectrum, forming a two-dimensional point scattering function that possesses shift-invariance. Subsequent to this, the power spectrum and the two-dimensional point scattering function undergo deconvolution using the Richardson–Lucy (R–L) iterative algorithm. The final stage involves calculating the signal azimuths and frequencies based on the deconvolution results from the preceding step. Comparative analyses involving simulations and sea test results reveal that the proposed method achieves a narrower main lobe width and diminished background noise in contrast to traditional FRAZ spectrum estimation techniques. This improvement is instrumental in minimizing the target’s energy leakage in both the azimuth and frequency domains.

Keywords

• deconvolution
• FRAZ spectrum
• line spectrum estimation
• array signal processing
• uniform linear array
• Richardson–Lucy algorithm